Metamaterial-based wideband rat-race hybrid coupler using slow wave lines

Based on derived convenient design equations for slow wave transmission lines and metamaterial line, a very compact and wideband rat-race hybrid coupler is proposed using three -90° slow wave lines and one -90° metamaterial line. The closed-form solutions for circuit parameters based on both phase and phase slope matching conditions are derived. At the design frequency of 2 GHz, the size of the proposed coupler is about 2.0 × 2.0 cm, which is a 85% reduction compared with the conventional one. In addition, the phase balance bandwidths based on ∠S₂₁-∠S₃₁ (0±10°) and ∠S₂₄-∠S₃₄ (180±10°) have been found to be 150 and 125%, which are 1.8 and 3.0 times improvements compared with those of the conventional one. The measured results are in reasonable agreement with the circuit- and EM-simulated ones.